We have so far $\mathbb{F}_8$, realized so that $t$ is a generator of the multiplicative group
$\mathbb{F}_8^\times$ with $7=(8-1)$ elements. Starting from it, we can extend, by explicitly introducing also a root of order nine (but not $3$) of unity. So that we have one of order $63=(8-1)(8+1)=64-1$.